Multicriticality in Yang-Lee edge singularity

TL;DR

This paper investigates non-unitary deformations of the 2D Tricritical Ising Model with imaginary magnetic fields, identifying two universality classes linked to Yang-Lee edge singularities and supported by numerical and theoretical analysis.

Contribution

It establishes two distinct universality classes of infrared fixed points in non-unitary deformations of the tricritical Ising model, connecting them to specific minimal models and verifying via numerical methods.

Findings

Identification of two universality classes: Yang-Lee and tricritical Yang-Lee.

Supported by PT symmetry considerations and c-theorem extensions.

Numerical verification using truncated conformal space approach.

Abstract

In this paper we study the non-unitary deformations of the two-dimensional Tricritical Ising Model obtained by coupling its two spin Z2 odd operators to imaginary magnetic fields. Varying the strengths of these imaginary magnetic fields and adjusting correspondingly the coupling constants of the two spin Z2 even fields, we establish the presence of two universality classes of infrared fixed points on the critical surface. The first class corresponds to the familiar Yang-Lee edge singularity, while the second class to its tricritical version. We argue that these two universality classes are controlled by the conformal non-unitary minimal models M(2,5) and M(2,7) respectively, which is supported by considerations based on PT symmetry and the corresponding extension of Zamolodchikov's c-theorem, and also verified numerically using the truncated conformal space approach. Our results are in agreement with a previous numerical study of the lattice version of the Tricritical Ising Model [1]. We also conjecture the classes of universality corresponding to higher non-unitary multicritical points obtained by perturbing the conformal unitary models with imaginary coupling magnetic fields.